Fully Funded EPSRC DTP PhD Studentship in Applied and Computational Mathematics
Project Summary
So much of the natural and man-made world is composed of collections of discrete
solid grains. However, there is currently no completely satisfactory theory to
describe their motion, en masse, in the many complex flow scenarios which are
important across industry and geophysics. Despite the challenges, a promising
paradigm has been building over the last 20 years. Based around key
experimental, mathematical and physical insights, continuum models for both the
flow of dry grains and for particles suspended in a background fluid are
beginning to mature.
In this project, the driving goal will be to develop a unified rheology spanning
the many flow regimes that particulate materials can exhibit. Once this model
begins to take shape, novel numerical methods will be developed to solve the
resultant dynamical equations. This in-house code will then be applied to
various test cases inspired by flows in nature, such as debris avalanches and
subsea landslides, and in industry, such as hopper flows and drum mixers.
The work will be framed and motivated by key open questions such as "Is it
useful in modelling to categorise particle flow dynamics into gas-like, liquid-
like and solid-like behaviour?", "What is the most appropriate numerical method
to solve multi-regime particulate flow equations?" and "How does the presence of
liquid water modify the severity of natural hazards and the efficiency of
industrial processes?".
Research Environment
Students undertaking this project will work in a dynamic field of research with
many opportunities for innovation and impact. Success in the project will see
the student gain ability and confidence in many areas of applied mathematics. In
particular, the student will work at the forefront of continuum mechanics,
computational fluid dynamics, granular rheology, discrete element modelling,
geophysics and engineering.
Cardiff’s School of Mathematics is home to a world-leading Applied Mathematics
group which has fostered an outstanding postgraduate research environment. The
latest Postgraduate Research Experience Survey (PRES) ranks it 3rd in overall
satisfaction and 1st (out of 22 in the UK) in professional development. With
around 15 full-time staff and PhD students and weekly seminars by international
experts, there will be many opportunities for knowledge exchange and guidance
throughout the project.
The successful candidate will also become member of a vibrant postgraduate
research community, which hosts the SIAM-IMA Student Chapter at Cardiff
University, formed by the Society for Industrial and Applied Mathematics and
supported by the Institute of Mathematics and its Applications. They will be
provided with a desk and a computer, and access to state-of-the-art facilities
in the School’s purpose-built new home, Abacws, where the School moved in
September 2021.
Training and Development Opportunities
With the funding enabled by this studentship, students will have access to many
conferences and workshops outside Cardiff. Of particular relevance in the coming
years are the Particles 2023 conference in Milan, the 2024 Gordon Research
Conference in Boston and Powders & Grains 2025 in India. These activities will
encourage the general intellectual and personal development of the student,
leading to many transferrable skills.
To expand their mathematical knowledge beyond that offered by their specific
project, in addition to research work, in the first two years the student will
attend a total of 100 hours of postgraduate lecture courses run by MAGIC
(Mathematics Access Grid Instruction and Collaboration), which is jointly
organised remotely by 20 UK Universities. Assignments to the MAGIC courses will
be assessed by the course lecturers.
HOW TO APPLY
Applicants should apply through the Cardiff University online application portal
(https://www.cardiff.ac.uk/study/postgraduate/research/programmes/programme/math
ematics), for a Doctor of Philosophy in Mathematics with an entry point of
October 2023.
In the research proposal section of your application, please specify the project
title and supervisors of this project. There is no requirement to submit a
detailed research proposal.
In the funding section, please select "I will be applying for advertised funding
from EPRSC DTP.
ACADEMIC CRITERIA
A 1st or upper 2nd class UK Honours degree (or equivalent) or a Master’s degree
is required in mathematics or a related subject.
ENGLISH LANGUAGE REQUIREMENTS
Applicants for whom English is not their first language must demonstrate
proficiency by obtaining an IELTS score of at least 6.5 overall, with a minimum
of 5.5 in each skills component. Further acceptable qualifications can be found
at https://www.cardiff.ac.uk/study/international/english-language-
requirements/postgraduate
SUPPORTING DOCUMENTS
· Curriculum vitae
· A personal statement
· Two completed references
· Degree certificates and transcripts
· Proof of English language (if applicable)
ELLIGIBILITY
EPSRC DTP studentships are available to home and international students. Up to
30% of our cohort can comprise international students, once the limit has been
reached we are unable to make offers to international students.
International students will not be charged the fee difference between the UK and
international rate. Applicants should satisfy the UKRI eligibility requirements.
Cardiff University is committed to support students from a range of backgrounds
and circumstances. Where needed, we will work with you to take into
consideration reasonable project adaptations (for example to support caring
responsibilities, disabilities, other significant personal circumstances) as
well as flexible working and part‐time study requests, to enable greater access
to a PhD. All our supervisors support us with this aim, so please feel
comfortable in discussing further with the listed PhD project supervisor to see
what is feasible.
Cardiff University is committed to supporting and promoting equality and
diversity and to creating an inclusive environment for all. We welcome
applications from all members of the global community irrespective of age,
disability, sex, gender identity, gender reassignment, marital or civil
partnership status, pregnancy or maternity, race, religion or belief and sexual
orientation.
We welcome applications for both full and part-time study and from candidates
with non-traditional academic backgrounds. For further information about modes
of study, please contact us.
ASSESSMENT
Applicants are reminded to submit all relevant documents (transcripts,
supporting statement, etc) by the deadline. Due to the volume of applications
received, incomplete applications will not be considered. Shortlisted applicants
will be invited to interview early in March 2023.
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